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FINALTERM EXAMINATION Spring 2010
Question No: 1 ( Marks: 1 ) - Please choose one
An optimization problem is one in which you want to find, ► Not a solution ► An algorithm ► Good solution ► The best solution Question No: 2 ( Marks: 1 ) - Please choose one
Although it requires more complicated data structures, Prim's algorithm for a minimum spanning tree is better than Kruskal's when the graph has a large number of vertices. ► True ► False Question No: 3 ( Marks: 1 ) - Please choose one
If a problem is in NP, it must also be in P. ► True ► False ► unknown Question No: 4 ( Marks: 1 ) - Please choose one
What is generally true of Adjacency List and Adjacency Matrix representations of graphs? ► Lists require less space than matrices but take longer to find the weight of an edge (v1,v2) ► Lists require less space than matrices and they are faster to find the weight of an edge (v1,v2) ► Lists require more space than matrices and they take longer to find the weight of an edge (v1,v2) ► Lists require more space than matrices but are faster to find the weight of an edge (v1,v2) Question No: 5 ( Marks: 1 ) - Please choose one
If a graph has v vertices and e edges then to obtain a spanning tree we have to delete ► v edges. ► v – e + 5 edges ► v + e edges. ► None of these
Question No: 6 ( Marks: 1 ) - Please choose one
Maximum number of vertices in a Directed Graph may be |V2| ► True ► False Question No: 7 ( Marks: 1 ) - Please choose one
The Huffman algorithm finds a (n) _____________ solution. ► Optimal ► Non-optimal ► Exponential ► Polynomial Question No: 8 ( Marks: 1 ) - Please choose one
The Huffman algorithm finds an exponential solution ► True ► False Question No: 9 ( Marks: 1 ) - Please choose one
The Huffman algorithm finds a polynomial solution ► True ► False Question No: 10 ( Marks: 1 ) - Please choose one
The greedy part of the Huffman encoding algorithm is to first find two nodes with larger frequency. ► True ► False Question No: 11 ( Marks: 1 ) - Please choose one
The codeword assigned to characters by the Huffman algorithm have the property that no codeword is the postfix of any other. ► True ► False Question No: 12 ( Marks: 1 ) - Please choose one
Huffman algorithm uses a greedy approach to generate a postfix code T that minimizes the expected length B (T) of the encoded string. ► True
► False Question No: 13 ( Marks: 1 ) - Please choose one
Shortest path problems can be solved efficiently by modeling the road map as a graph. ► True ► False Question No: 14 ( Marks: 1 ) - Please choose one
Dijkestra’s single source shortest path algorithm works if all edges weights are non-negative and there are negative cost cycles. ► True ► False Question No: 15 ( Marks: 1 ) - Please choose one
Bellman-Ford allows negative weights edges and negative cost cycles. ► True ► False Question No: 16 ( Marks: 1 ) - Please choose one
The term “coloring” came form the original application which was in architectural design. ► True ► False Question No: 17 ( Marks: 1 ) - Please choose one
In the clique cover problem, for two vertices to be in the same group, they must be adjacent to each other. ► True ► False Question No: 18 ( Marks: 1 ) - Please choose one
Dijkstra’s algorithm is operates by maintaining a subset of vertices ► True ► False Question No: 19 ( Marks: 1 ) - Please choose one
The difference between Prim’s algorithm and Dijkstra’s algorithm is that Dijkstra’s algorithm uses a different key. ► True
► False Question No: 20 ( Marks: 1 ) - Please choose one
Consider the following adjacency list:
Which of the following graph(s) describe(s) the above adjacency list?
►
►
►
► Question No: 21 ( Marks: 1 ) - Please choose one
We do sorting to, ► keep elements in random positions ► keep the algorithm run in linear order ► keep the algorithm run in (log n) order ► keep elements in increasing or decreasing order Question No: 22 ( Marks: 1 ) - Please choose one
After partitioning array in Quick sort, pivot is placed in a position such that ► Values smaller than pivot are on left and larger than pivot are on right ► Values larger than pivot are on left and smaller than pivot are on right ► Pivot is the first element of array ► Pivot is the last element of array Question No: 23 ( Marks: 1 ) - Please choose one
Merge sort is stable sort, but not an in-place algorithm ► True ► False Question No: 24 ( Marks: 1 ) - Please choose one
In counting sort, once we know the ranks, we simply _________ numbers to their final positions in an output array. ► Delete ► copy ► Mark ► arrange Question No: 25 ( Marks: 1 ) - Please choose one
Dynamic programming algorithms need to store the results of intermediate sub-problems. ► True ► False Question No: 26 ( Marks: 1 ) - Please choose one
A p × q matrix A can be multiplied with a q × r matrix B. The result will be a p × r matrix C. There are (p . r) total entries in C and each takes _________ to compute. ► O (q) ► O (1) ► O (n2) ► O (n3) Question No: 27 ( Marks: 2 )
Give a detailed example for 2-d maxima problem.
Let took a point p in 2-dimensional space given by its integer coordinates, p = (p.x, p.y).
A point p is said to dominated by point q if p.x ≤ q.x and p.y ≤ q.y. Given a set of n points, P = {p1, p2, . . . , pn} in 2-space a point is said to be maximal if it is not dominated by any other point in P.
The problem is to output all the maximal points of P. A brute-force algorithmthat ran in Θ(n2) time is used in it. It operated by comparing all pairs of points. the brute-force algorithm uses no intelligence in pruning out decisions. For example, once we know that a point pi is dominated by another point pj, we do not need to use pi for eliminating other points. This follows from the fact that dominance relation is transitive. If pj dominates pi and pi dominates ph then pj also dominates ph; pi is not needed. Question No: 28 ( Marks: 2 )
Differentiate between back edge and forward edge.
For directed graphs edges r classified as:Back edge: (u, v) where v is an ancestor of u in the tree.Forward edge: (u, v) where v is a proper descendent of u in the tree.Cross edge: (u, v) where u and v are not ancestor or descendent of one another. In fact, the edge may go between different trees of the forest.
Question No: 29 ( Marks: 2 )
How the generic greedy algorithm operates in minimum spanning tree?
Ans:In undirected, connected graph whose edges have numeric weights areG = (V, E)Here’s applying generic greedy algorithm operates in minimum spanning tree is simple. we maintain a subset of edges E of the graph .
This subset is A.
Initially, A is empty. We will add edges one at a time until A equals the MST.A subset A E is viable if A is a subset of edges of some MST. An edge (u, v) E − A is safe ifA {(u, v)} is viable. In other words, the choice (u, v) is a safe choice to add so that A can still be extended to form a MST. if A is viable, it cannot contain a cycle. A generic greedy algorithm operates by repeatedly adding any safe edge to the current spanning tree. Question No: 30 ( Marks: 2 )
What are two cases for computing assuming we already have the previous matrix
using Floyed-Warshall algorithm?
Ans:The two cases for computing assuming we already have the previous matrix using Floyed-Warshall algorithm are:
1. Don’t go through vertex k at all.2. Do go through vertex k
Question No: 31 ( Marks: 3 )
Describe Minimum Spanning Trees Problem with examples. Question No: 32 ( Marks: 3 )
What is decision problem, also explain with example?
Ans:A problem is called a decision problem if its output is a simple
yes or no true/false, 0/1, Accept/reject.)
For example:The MST decision problem would be a decision problem, Given a weighted graph G and an integer k, does G have a spanning tree whose weight is at most k? Question No: 33 ( Marks: 3 )
Prove that the generic TRAVERSE (S) marks every vertex in any connected graph exactly once and the set of edges (v, parent (v)) with parent (v) ¹ F form a spanning tree of the graph.
Ans:Proof:it should be sured that no vertex is marked more than once. The algorithm marks s. Letv = s be a vertex and let s → · · · → u → v be a path from s to v with the minimum number of edges.Since the graph is connected, such a path always exists. If the algorithm marks u, then it must put (u, v) into the bag, so it must take (u, v) out of the bag at which point v must be marked. Thus, by induction on the shortest path distance from s, the algorithm marks every vertex in the graph.Call an edge (v, parent(v)) with parent(v) = ∅, a parent edge. For any node v, the path of parent edges v → parent(v) → parent(parent(v)) → . . . eventually leads back to s. So the set of parent edges form a connected graph.both end points of every parent edge are marked, and the number of edges is exactly one less than the number of vertices. Thus, the parent edges form a spanning tree. Question No: 34 ( Marks: 5 )
Suppose you could reduce an NP-complete problem to a polynomial time problem in polynomial time. What would be the consequence? Question No: 35 ( Marks: 5 )
Prove the following lemma,Lemma: Given a digraph G = (V, E), consider any DFS forest of G and consider any edge (u, v) ∈ E. If this edge is a tree, forward or cross edge, then f[u] > f[v]. If this edge is a back edge, then f[u] ≤ f[v]
Ans:Proof:
For the non-tree forward and back edges the proof follows directly from the parenthesis lemma.For example, for a forward edge (u, v), v is a descendent of u and so v’s start-finish interval is contained within u’s implying that v has an earlier finish time.
For a cross edge (u, v) the two time intervals are disjoint. When we were processing u, v was not white (otherwise (u, v) would be a tree edge), implying that v was started before u. Because the intervals are disjoint, v must have also finished before u. Question No: 36 ( Marks: 5 )
What is the cost of the following graph?
Pseudo code of DFS 5
Ans:DFS procedure can be written
1. recursively or 2. non-recursively.
RECURSIVEDFS(v) if (v is unmarked )
then mark v for each edge (v,w) do RECURSIVEDFS(w)
ITERATIVEDFS(s)PUSH(s)while stack not emptydo v ← POP()if v is unmarkedthen mark vfor each edge (v,w)do PUSH(w)
and prove the DFS algorithm 5
Total 36 Questions,
26 MCQ’s
Using ASCII standard the string abacdaacac will be encoded with __________ bits.80160320100
Using ASCII standard the string abacdaacac will be encoded with 160 bits.TrueFalse
Using ASCII standard the string abacdaacac will be encoded with 320 bits.TrueFalse
Using ASCII standard the string abacdaacac will be encoded with 100 bits.
TrueFalse
Please choose oneConsider the following Huffman TreeThe binary code for the string TEA is
10 00 010011 00 01010 00 11011 10 110
The book written by Al-KhwarzamiHisab al-jabr w'al mugabalah
The Huffman algorithm finds a (n) _____________ solution. ► Optimal ► Non-optimal ► Exponential ► Polynomial
Huffman algorithm uses a greedy approach to generate a postfix code T that minimizes the expected length B (T) of the encoded string. ► True ► False
The difference between Prim’s algorithm and Dijkstra’s algorithm is that Dijkstra’s algorithm uses a different key. ► True ► False
4 Questions of 2 Marks1. Difference between Prim’s algorithm and Dijikstra’s algorithm.
Ans:
The difference between Prim’s algorithm and Dijkstra’s algorithm is that Dijkstra’s algorithm uses a different key.
2. What is coloring problem?3. Is it better that we using brute force approach to solve knap sack
problem, can we do better.
3 Questions of 3 Marks
1. following is the list of adjacency vertex, Identify that is any vertex have isolated property.
a-------b--cb------d--ee------f--dc-----b---ff----bg
2. How Dijikstra’s algorithm operate, give an example.
3 Questions of 5 Marks.
1. What is the reduction, Explain with example. (From Last chapter of handsout)
2. Describe the Minimum spanning Tree with example.
3. What is the cost of following Graph.
1: What is the time complexity to extract a vertex from the priority queue in Prim’s algorithm?
log (v) v.v e.e log(e)
2: Which statement is true?
If a dynamic-programming problem satisfies the optimal-substructure property, then a locally optimal solution is globally optimal.
If a greedy choice property satisfies the optimal-substructure property, then a locally optimal solution is globally optimal.
both of above none of above
3: Kruskal's algorithm (choose best non-cycle edge) is better than Prim's (choose best tree edge) when the graph has relatively few edges.
True False
4: You have an adjacency list for G, what is the time complexity to compute Graph transpose G^T ?
V+e v.e v e
5: What general property of the list indicates that the graph has an isolated vertex? There is Null pointer at the end of list. The Isolated vertex is not handled in list. Only one value is entered in the list. There is at least one null list.
6: Which is true statement.
Breadth first search is shortest path algorithm that works on un-weighted graphs. Depth first search is shortest path algorithm that works on un-weighted graphs. Both of above are true. None of above are true.
7: A dense undirected graph is: A graph in which E = O(V^2) A graph in which E = O(V) A graph in which E = O(log V) All items above may be used to characterize a dense undirected graph.
8: What is generally true of Adjacency List and Adjacency Matrix representations of graphs?
Lists require less space than matrices but take longer to find the weight of an edge (v1,v2)
Lists require less space than matrices and they are faster to find the weight of an edge (v1, v2)
Lists require more space than matrices and they take longer to find the weight of an edge (v1, v2).
9: Suppose that a graph G = (V,E) is implemented using adjacency lists. What is the complexity of a breadth-first traversal of G?
O(|V |^2) O(|V | |E|) O(|V |^2|E|) O(|V | + |E|)
10: The relationship between number of back edges and number of cycles in DFS is,
Both are equal Back edges are half of cycles Back edges are one quarter of cycles There is no relationship between no. of edges and cycles
11: Using ASCII standard the string “abacdaacacwe” will be encoded with __________ bits
64 128 96 120
12: What is the time complexity to extract a vertex from the priority queue in Prim’s algorithm?
log (V)
v.v e.e log
13: the analysis of selection algorithm shows the total running time is indeed------------in n.
arithmetic geometric linear orthogonal
14: back edge is
(1) In Prim’s algorithm, the additional information maintained by the algorithm is the length of the shortest edge from vertex v to points already in the tree.
A) TRUEB) FALSEC) UNKNOWN
(2) Although it requires more complicated data structures, Prim's algorithm for aminimum spanning tree is better than Kruskal's when the graph has a large number ofvertices.A) TRUE.B) FALSEC: UNKNOWN
(3) If a problem is NP-complete, it must also be in NP.A) TRUE.B) FALSEC) UNKNOWN
(4) What is the worst-case runtime complexity of the following C functionint function(int n){int i, j, k;k = n;for(i=-100; i<10*log(n);i++){k = k/2;} for(j=i; j> n; j--){k=j/2;}rreturn k;}
What order is the execution of this codea) O(log n)
b) O(n)c) O(n log n)d) O(n2)e) O(n2 log n)
(4) Which statement is true(I) The running time of Bellman-Ford algorithm is T (VE)(II) Both Dijkstra’s algorithm and Bellman-Ford are based on performing repeated relaxations(III) The 0-1 knapsack problem is hard to solve
• Only I• Only III• Both I and III• All of these
5) Which of the following arrays represent descending (max) heaps?I. [10,7,7,2,4,6]II. [10,7,6,2,4,7]III. [10,6,7,2,4,6]IV. [6,6,7,2,4,10]
• Only II• Only IV• Both II and IV• Both I and III
6. Which of the following statement(s) is/are correct?(a) O(n log n + n2) = O(n2).(b) O(n log n + n2) = O(n2 log 2n)(c) O(c n2) = O(n2) where c is a constant.(d) O(c n2) = O(c) where c is a constant.(e) O(c) = O(1) where c is a constant.
Only (a) & (e) Both (c) and (e)
7. Which of the shortest path algorithms would be most appropriate for finding paths in the graph with negative edge weights and cycles?I.Dijkstra’s AlgorithmII. Bellman-Ford AlgorithmIII. Floyd Warshall Algorithm
Only II Only III Both II & III
8. Which of the following orders is not a possible order in which Depth First Search can visit the vertices of the directed graph shown below?
• ABCEFD• ACEBFD• ADFEBC• ADFBCE• ABFECD
9. Suppose we have two problems A and B .Problem A is polynomial-time reducible and problem B is NP-complete. If we reduce problem A into B then problem A becomes NP-complete
• Yes• No
10. How can the number of strongly connected components of a graph change if a new edge is added?
The number of strongly connected components can be increased. The number of strongly connected components can be reduced. No change will occur. None of these.
11. The recurrence relation of Tower of Hanoi is given below? 1 if n =1T n =?-133( )2 (T n- +1) 1if n>1In order to move a tower of 6 rings from one peg to another, how many moves arerequired?
15 7 63 32
12. Edge (u, v) is a forward edge if
u is a proper descendant of v in the tree v is a proper descendant of u in the tree None of these
13. Is 22n= O? 2n -26? ?
Yes it is possible No it is not possible None of these
14. If, in a DFS forest of digraph G = (V, E), f[u] = f[v] for an edge (u, v) ? E then the edge is called
Back edge Forward edge Cross Edge Tree Edge None of these
15. How can the number of strongly connected components of a graph change if a new edge is added?
The number of strongly connected components can be increased. The number of strongly connected components can be reduced. No change will occur. None of these.
16. Best and worst case times of an algorithm may be same. True False
17. Can an adjacency matrix for a directed graph ever not be square in shape? Yes No
18. If an algorithm has a complexity of 2n2+ 4n + 3 for some model of computation (some set of assumptions) and some complexity measures (such as number of comparisonoperations) we could say that it has complexity(a) O(log2n)(b) O(n2)(c) O(2 + 4 + 3)(d) all of the above(e) none of the above
1. In which order we can sort? increasing order only decreasing order only increasing order or decreasing order both at the same time
2. heap is a left-complete binary tree that conforms to the ___________ increasing order only decreasing order only heap order (log n) order
3. In the analysis of Selection algorithm, we make a number of passes, in fact it could be as many as,
T(n) T(n / 2) log n n / 2 + n / 4
4. How much time merge sort takes for an array of numbers? T(n^2) T(n) T( log n) T(n log n)
5. One of the clever aspects of heaps is that they can be stored in arrays without using any _______________.
pointers constants variables functions
6. the analysis of Selection algorithm, we eliminate a constant fraction of the array with each phase; we get the convergent _______________ series in the analysis
linear arithmetic geometric exponent
7:. Sieve Technique applies to problems where we are interested in finding a single item from a larger set of _____________
n items phases pointers constant
8. The sieve technique works in ___________ as follows
phases numbers integers routines
9. For the heap sort, access to nodes involves simple _______________ operations. arithmetic binary algebraic logarithmic
10. The analysis of Selection algorithm shows the total running time is indeed ________in n,
arithmetic geometric linear orthogonal
11. Divide-and-conquer as breaking the problem into a small number of pivot Sieve smaller sub problems Selection
12. Slow sorting algorithms run in, T(n^2) T(n) T( log n) T(n log n)
13. A heap is a left-complete binary tree that conforms to the increasing order only decreasing order only heap order (log n) order
14. For the heap sort we store the tree nodes in level-order traversal in-order traversal pre-order traversal post-order traversal
15. The reason for introducing Sieve Technique algorithm is that it illustrates a very important special case of,
divide-and-conquer, decrease and conquer greedy nature
2-dimension Maxima
16. We do sorting to, Select correct option:
keep elements in random positions keep the algorithm run in linear order keep the algorithm run in (log n) order keep elements in increasing or decreasing order
17. Sorting is one of the few problems where provable ________ bonds exits on how fast we can sort,Select correct option:
upper lower average log n
For the heap sort we store the tree nodes inSelect correct option:
level-order traversal in-order traversal pre-order traversal post-order traversal
18: For the Sieve Technique we take time T(nk) T(n / 3) n^2 n/3
20: In Sieve Technique we do not know which item is of interest Select correct option:
True False
21: Slow sorting algorithms run in, T(n^2) T(n) T( log n) T(n log n)
22: Divide-and-conquer as breaking the problem into a small number of pivot Sieve smaller sub problems Selection
23: For the sieve technique we solve the problem,
recursively mathematically precisely accurately
24: we do sorting to,
keep elements in random positions keep the algorithm run in linear order keep the algorithm run in (log n) order keep elements in increasing or decreasing order
25: The reason for introducing Sieve Technique algorithm is that it illustrates a very important special case of,
divide-and-conquer decrease and conquer greedy nature 2-dimension Maxima
26: In Sieve Technique we donot know which item is of interest
true false
27: In the analysis ofSelection algorithm, we make a number of passes, in fact it could be as many as,
T(n) T(n / 2) log n n / 2 + n / 4
28: Divide-and-conquer as breaking the problem into a small number of
pivot Sieve smaller sub problems Selection
29: A heap is a left-complete binary tree that conforms to the ___________
increasing order only decreasing order only heap order (log n) order
30: Slow sorting algorithms run in,
T(n^2) T(n) T( log n) T(n log n)
31: One of the clever aspects of heaps is that they can be stored in arrays without using any _______________.
pointers constants variables functions
32: Sorting is one of the few problems where provable ________ bonds exits on how fast we can sort,
upper lower average log n
33: For the sieve technique we solve the problem,
mathematically precisely accurately recursively
34: Sieve Technique can be applied to selection problem?
True False
35: How much time merge sort takes for an array of numbers?
(n^2) T(n) T( log n)
T(n log n)
36; : For the Sieve Technique we take time
T(nk) T(n / 3) n^2 n/3
37: Heaps can be stored in arrays without using any pointers; this is due to the ____________ nature of the binary tree,
left-complete right-complete tree nodes tree leaves
38: How many elements do we eliminate in each time for the Analysis of Selection algorithm?
n / 2 elements (n / 2) + n elements n / 4 elements 2 n elements
39: We do sorting to,
keep elements in random positions keep the algorithm run in linear order keep the algorithm run in (log n) order keep elements in increasing or decreasing order
40: In which order we can sort?
increasing order only decreasing order only increasing order or decreasing order both at the same time
41: : In the analysis of Selection algorithm, we make a number of passes, in fact it could be as many as,
T(n) T(n / 2) log n n / 2 + n / 4
42: The sieve technique is a special case, where the number of sub problems is just
5 Many 1 few
Question No: 1 ( Marks: 1 ) - Please choose one
Random access machine or RAM is a/an ► Machine build by Al-Khwarizmi ► Mechanical machine ► Electronics machine ► Mathematical model Question No: 2 ( Marks: 1 ) - Please choose one
_______________ is a graphical representation of an algorithm ► notation ► notation ► Flowchart ► Asymptotic notation Question No: 3 ( Marks: 1 ) - Please choose one
A RAM is an idealized machine with ______________ random-access memory. ► 256MB ► 512MB ► an infinitely large ► 100GB Question No: 4 ( Marks: 1 ) - Please choose one
What type of instructions Random Access Machine (RAM) can execute? Choose best answer ► Algebraic and logic ► Geometric and arithmetic ► Arithmetic and logic ► Parallel and recursive Question No: 5 ( Marks: 1 ) - Please choose one
What will be the total number of max comparisons if we run brute-force maxima algorithm with n elements?
► 2n
► 2
n
n ► n ► 8n Question No: 6 ( Marks: 1 ) - Please choose one
What is the solution to the recurrence T(n) = T(n/2)+n .
► O(logn) ► O(n) ► O(nlogn) ► O(n2) Question No: 7 ( Marks: 1 ) - Please choose one
Consider the following code:For(j=1; j<n;j++)
For(k=1; k<15;k++)For(l=5; l<n; l++){
Do_something_constant();}
What is the order of execution for this code. ► O(n) ► O(n3) ► O(n2 log n) ► O(n2) Question No: 8 ( Marks: 1 ) - Please choose one
Consider the following Algorithm:Factorial (n){ if (n=1) return 1 else return (n * Factorial(n-1))}Recurrence for the following algorithm is: ► T(n) = T(n-1) +1 ► T(n) = nT(n-1) +1 ► T(n)= T(n-1) +n ► T(n)=T(n(n-1)) +1 Question No: 9 ( Marks: 1 ) - Please choose one
What is the total time to heapify? ► Ο(log n) ► Ο(n log n) ► Ο(n2 log n) ► Ο(log2 n) Question No: 10 ( Marks: 1 ) - Please choose one
When we call heapify then at each level the comparison performed takes time ► It will take Θ (1) ► Time will vary according to the nature of input data ► It can not be predicted ► It will take Θ (log n) Question No: 11 ( Marks: 1 ) - Please choose one
In Quick sort, we don’t have the control over the sizes of recursive calls ► True ► False ► Less information to decide ► Either true or false Question No: 12 ( Marks: 1 ) - Please choose one
Is it possible to sort without making comparisons? ► Yes ► No Question No: 13 ( Marks: 1 ) - Please choose one
If there are Θ (n2) entries in edit distance matrix then the total running time is ► Θ (1) ► Θ (n2) ► Θ (n) ► Θ (n log n) Question No: 14 ( Marks: 1 ) - Please choose one
For Chain Matrix Multiplication we can not use divide and conquer approach because, ► We do not know the optimum k ► We use divide and conquer for sorting only ► We can easily perform it in linear time ► Size of data is not given
Question No: 15 ( Marks: 1 ) - Please choose one
The Knapsack problem belongs to the domain of _______________ problems. ► Optimization ► NP Complete ► Linear Solution ► Sorting Question No: 16 ( Marks: 1 ) - Please choose one
Suppose we have three items as shown in the following table, and suppose the capacity of the knapsack is 50 i.e. W = 50.
Item Value Weight1 60 102 100 203 120 30
The optimal solution is to pick ► Items 1 and 2 ► Items 1 and 3 ► Items 2 and 3 ► None of these
3. ______________ graphical representation of algorithm.
> asymptotic
>. flowchart
4. who invented the quick sort
C.A.R. Hoare
5. function is given like 4n^4+ 5n^3+n what is the run time of this
(n^4) (n^3) (4n^4+ 5n^3) (4n^4+ 5n^3)
6. main elements to a divide-and-conquer
Divide---->conquer---------->combine
7. T(n)={4 if n=1, otherwise T(n/5)+3n^2
what is the answer if n=5
answer is 79
8. Merge sort is a stable algorithm but not an in-place algorithm.
>True
>false
_______________ is a graphical representation of an algorithm notation Flowchart Asymptotic notation
notation
Question No: 2 ( Marks: 1 ) - Please choose one
Which of the following is calculated with Big o notation? Lower bounds Upper bounds Both upper and lower bound Medium bounds
Question No: 3 ( Marks: 1 ) - Please choose one Merge sort makes two recursive calls. Which statement is true after these recursive calls finish, but before the merge step?
The array elements form a heap Elements in each half of the array are sorted amongst themselves Elements in the first half of the array are less than or equal to elements in the second half of the array None of the above
Question No: 4 ( Marks: 1 ) - Please choose one Who invented Quick sort procedure?
Hoare Sedgewick Mellroy Coreman
Question No: 5 ( Marks: 1 ) - Please choose one What is the solution to the recurrence T(n) = T(n/2)+n, T(1) = 1
O(logn) O(n) O(nlogn) O(2n)
FINALTERM EXAMINATIONFall 2008CS502- Fundamentals of Algorithms (Session - 1)Marks: 75Question No: 1 ( Marks: 1 ) - Please choose one_______________ is a graphical representation of an algorithmnotationFlowchartAsymptotic notationnotation
Question No: 2 ( Marks: 1 ) - Please choose oneWhich of the following is calculated with Bigo notation?Lower boundsUpper boundsBoth upper and lower boundMedium bounds
Question No: 3 ( Marks: 1 ) - Please choose oneMerge sort makes two recursive calls. Which statement is true after these recursive callsfinish, but before the merge step?The array elements form a heapElements in each half of the array are sorted amongst themselvesElements in the first half of the array are less than or equal to elements in thesecond half of the arrayNone of the above
Question No: 4 ( Marks: 1 ) - Please choose oneWho invented Quick sort procedure?HoareSedgewickMellroyCoreman
Question No: 5 ( Marks: 1 ) - Please choose oneWhat is the solution to the recurrence T(n) = T(n/2)+n, T(1) = 1O(logn)O(n)O(nlogn)
O(2n)
Question No: 6 ( Marks: 1 ) - Please choose one(Huffman tree is missing)Consider the following Huffman TreeThe binary code for the string TEA is10 00 010011 00 01010 00 11011 10 110
Question No: 7 ( Marks: 1 ) - Please choose oneIf a graph has v vertices and e edges then to obtain a spanning tree we have to deletev edges.v e + 5 edgesv + e edges.None of these
Question No: 8 ( Marks: 1 ) - Please choose oneCan an adjacency matrix for a directed graph ever not be square in shape?YesNo
Question No: 9 ( Marks: 1 ) - Please choose oneOne of the clever aspects of heaps is that they can be stored in arrays without using any_______________.Pointersconstantsvariablesfunctions
Question No: 10 ( Marks: 1 ) - Please choose oneMerge sort requires extra array storage,TrueFalse
Question No: 11 ( Marks: 1 ) - Please choose oneNon-optimal or greedy algorithm for money change takes____________O(k)O(kN)
O(2k)O(N)
Question No: 12 ( Marks: 1 ) - Please choose oneThe Huffman codes provide a method of encoding data inefficiently when coded usingASCII standard.TrueFalse
Question No: 13 ( Marks: 1 ) - Please choose oneUsing ASCII standard the string abacdaacac will be encoded with __________ bits.80160320100
Question No: 14 ( Marks: 1 ) - Please choose oneUsing ASCII standard the string abacdaacac will be encoded with 160 bits.TrueFalse
Question No: 15 ( Marks: 1 ) - Please choose oneUsing ASCII standard the string abacdaacac will be encoded with 320 bits.TrueFalse
Question No: 16 ( Marks: 1 ) - Please choose oneUsing ASCII standard the string abacdaacac will be encoded with 100 bits.TrueFalse
Question No: 17 ( Marks: 1 ) - Please choose oneUsing ASCII standard the string abacdaacac will be encoded with 32 bytesTrueFalse
Question No: 18 ( Marks: 1 ) - Please choose oneThe greedy part of the Huffman encoding algorithm is to first find two nodes withsmallest frequency.
TrueFalse
Question No: 19 ( Marks: 1 ) - Please choose one
The greedy part of the Huffman encoding algorithm is to first find two nodes withcharacter frequencyTrueFalse
Question No: 20 ( Marks: 1 ) - Please choose oneHuffman algorithm uses a greedy approach to generate an antefix code T that minimizesthe expected length B (T) of the encoded string.TrueFalse
Question No: 21 ( Marks: 1 ) - Please choose oneDepth first search is shortest path algorithm that works on un-weighted graphs.TrueFalse
Question No: 22 ( Marks: 1 ) - Please choose oneDijkestra s single source shortest path algorithm works if all edges weights are nonnegativeand there are no negative cost cycles.TrueFalse
Question No: 23 ( Marks: 1 ) - Please choose oneDijkestra s single source shortest path algorithm works if all edges weights are negativeand there are no negative cost cycles.
TrueFalse hb
Question No: 24 ( Marks: 1 ) - Please choose oneFloyd-Warshall algorithm is a dynamic programming algorithm; the genius of thealgorithm is in the clever recursive formulation of the shortest path problem.TrueFlase
Question No: 25 ( Marks: 1 ) - Please choose oneFloyd-Warshall algorithm, as in the case with DP algorithms, we avoid recursiveevaluation by generating a table forkij dTrueFlase
Question No: 26 ( Marks: 1 ) - Please choose oneThe term coloring came form the original application which was in map drawing.TrueFalse
Question No: 27 ( Marks: 1 ) - Please choose oneIn the clique cover problem, for two vertices to be in the same group, they must be_______________each other.Apart fromFar fromNear toAdjacent to
Question No: 28 ( Marks: 1 ) - Please choose oneIn the clique cover problem, for two vertices to be in the same group, they must be apartfrom each other.TrueFalse
Question No: 29 ( Marks: 1 ) - Please choose oneThe difference between Prim s algorithm and Dijkstra s algorithm is that Dijkstra salgorithm uses a different key.TrueFalse
Question No: 30 ( Marks: 1 ) - Please choose oneThe difference between Prim s algorithm and Dijkstra s algorithm is that Dijkstra salgorithm uses a same key.TrueFalse
Question # 1 of 10 ( Start time: 06:18:58 PM ) Total Marks: 1
We do sorting to, Select correct option:
keep elements in random positions keep the algorithm run in linear order keep the algorithm run in (log n) order keep elements in increasing or decreasing order
Question # 2 of 10 ( Start time: 06:19:38 PM ) Total Marks: 1 Heaps can be stored in arrays without using any pointers; this is due to the ____________ nature of the binary tree, Select correct option:
left-completeright-completetree nodes tree leaves Sieve Technique can be applied to selection problem? Select correct option:
True False
Question # 4 of 10 ( Start time: 06:21:10 PM ) Total Marks: 1 A heap is a left-complete binary tree that conforms to the ___________ Select correct option:
increasing order only decreasing order only heap order (log n) order Question # 5 of 10 ( Start time: 06:21:39 PM ) Total Marks: 1 A (an) _________ is a left-complete binary tree that conforms to the heap order Select correct option:
heapbinary tree binary search tree array
Question # 6 of 10 ( Start time: 06:22:04 PM ) Total Marks: 1 Divide-and-conquer as breaking the problem into a small number of Select correct option:
pivot
Sieve smaller sub problems Selection Question # 7 of 10 ( Start time: 06:22:40 PM ) Total Marks: 1 In Sieve Technique we do not know which item is of interest Select correct option:
True False
Question # 8 of 10 ( Start time: 06:23:26 PM ) Total Marks: 1 The recurrence relation of Tower of Hanoi is given below T(n)={1 if n=1 and 2T(n-1) if n >1 In order to move a tower of 5 rings from one peg to another, how many ring moves are required? Select correct option:
16 10 32 31 (yeh just tukkahai)
Question # 9 of 10 ( Start time: 06:24:44 PM ) Total Marks: 1 In the analysis of Selection algorithm, we eliminate a constant fraction of the array with each phase; we get the convergent _______________ series in the analysis, Select correct option:
lineararithmeticgeometric (yeh b gup hi lugtihai)exponent
Question # 10 of 10 ( Start time: 06:25:43 PM ) Total Marks: 1 For the heap sort, access to nodes involves simple _______________ operations. Select correct option:
arithmeticbinaryalgebraiclogarithmic (bongihai...)
Question No: 31 ( Marks: 1 )Do you think greedy algorithm gives an optimal solution to the activity schedulingproblem?yes, greedy algorithm gives an optimal solution to the activity scheduling
problem. as we have the data as a whole ,and activity a1 must be started at a given start time and ends at a given finish time. all the intermediate activities who overlap will be excluded automatically as no new activity will be selected as our data till the finish of last activity. so this greediness of algorithm gives us the optimal solution.
Question No: 32 ( Marks: 1 )Define Forward edge
A forward edge is a non-tree edge that connects a vertex to a descendent in a DFS-tree.
Question No: 33 ( Marks: 2 )Is there any relationship between number of back edges and number of cycles in DFS?
A back edge connects a vertex to an ancestor in a DFS-tree. No back edges means no cycles. But there is some simple relationship Between the number of back edges and the number of cycles. For example, a DFS tree may only have a single back edge, and there may anywhere from one up to an exponential number of simple cycles in the graph.
Question No: 34 ( Marks: 2 )What is the common problem in communications networks and circuit designing?
Common problem in communications networks and circuit design is that of connecting together a set of nodes by a network of total minimum length. The length is the sum of lengths of connecting wires.
Question No: 35 ( Marks: 3 )Let the adjacency list representation of an undirected graph is given below.Explain what general property of the list indicates that the graph has an isolatedvertex.a b c eb a dc a d e fd b c fe a c ff c d eg
Ans:A graph is connected if every vertex can reach
Every other vertex. and is isolated if any node has not connected to other vertex ,here’s “g” is the node that is not connected with any other vertex. This general property of the list indicates that the graph has an isolated vertex.
Algorithm-CS502QUIZ # 1
Mc09040076003-11-2010
MC090400760 : Imran Shahzad
Quiz Start Time: 11:20 PM
Time Left
35 sec(s)
Question # 1 of 10 ( Start time: 11:20:20 PM ) Total Marks: 1
The number of nodes in a complete binary tree of height h is
Select correct option:
MC090400760 : Imran Shahzad
Quiz Start Time: 11:20 PM
Time Left
81 sec(s)
Question # 2 of 10 ( Start time: 11:21:44 PM ) Total Marks: 1
A heap is a left-complete binary tree that conforms to the ___________
Select correct option:
MC090400760 : Imran Shahzad
Quiz Start Time: 11:20 PM
Time Left
79 sec(s)
Question # 3 of 10 ( Start time: 11:22:29 PM ) Total Marks: 1
In which order we can sort?
Select correct option:
MC090400760 : Imran Shahzad
Quiz Start Time: 11:20 PM
Time Left
8 sec(s)
Question # 4 of 10 ( Start time: 11:22:57 PM ) Total Marks: 1
Consider the following Algorithm: Fun(n){ if (n=1) return 1 else return (n * Fun(n-1)) } Recurrence for the above algorithm is:
Select correct option:
MC090400760 : Imran Shahzad
Quiz Start Time: 11:20 PM
Time Left
7 sec(s)
Question # 5 of 10 ( Start time: 11:24:25 PM ) Total Marks: 1
How much time merge sort takes for an array of numbers?
Select correct option:
MC090400760 : Imran Shahzad
Quiz Start Time: 11:20 PM
Time Left
17 sec(s)
Question # 6 of 10 ( Start time: 11:25:57 PM ) Total Marks: 1
Sieve Technique can be applied to selection problem?
Select correct option:
MC090400760 : Imran Shahzad
Quiz Start Time: 11:20 PM
Time Left
72 sec(s)
Question # 7 of 10 ( Start time: 11:27:23 PM ) Total Marks: 1
The reason for introducing Sieve Technique algorithm is that it illustrates a very important special case of,
Select correct option:
MC090400760 : Imran Shahzad
Quiz Start Time: 11:20 PM
Time Left
20 sec(s)
Question # 8 of 10 ( Start time: 11:27:57 PM ) Total Marks: 1
The analysis of Selection algorithm shows the total running time is indeed ________in n,
Select correct option:
MC090400760 : Imran Shahzad
Quiz Start Time: 11:20 PM
Time Left
42 sec(s)
Question # 9 of 10 ( Start time: 11:29:27 PM ) Total Marks: 1
For the Sieve Technique we take time
Select correct option:
MC090400760 : Imran Shahzad
Quiz Start Time: 11:20 PM
Time Left
23 sec(s)
Question # 10 of 10 ( Start time: 11:30:44 PM ) Total Marks: 1
How many elements do we eliminate in each time for the Analysis of Selection algorithm?
Select correct option:
Quiz Start Time: 06:18 PM Time Left 55 sec(s) Question # 1 of 10 ( Start time: 06:18:58 PM ) Total Marks: 1 We do sorting to, Select correct option: keep elements in random positions keep the algorithm run in linear order keep the algorithm run in (log n) order keep elements in increasing or decreasing order MC090406557 : Nadia Parveen Quiz Start Time: 06:18 PM Time Left 62 sec(s) Question # 2 of 10 ( Start time: 06:19:38 PM ) Total Marks: 1 Heaps can be stored in arrays without using any pointers; this is due to the ____________ nature of the binary tree, Select correct option: left-complete right-complete tree nodes
tree leaves MC090406557 : Nadia Parveen Quiz Start Time: 06:18 PM Time Left 77 sec(s) Question # 3 of 10 ( Start time: 06:20:18 PM ) Total Marks: 1 Sieve Technique can be applied to selection problem? Select correct option: True False MC090406557 : Nadia Parveen Quiz Start Time: 06:18 PM Time Left 74 sec(s) Question # 4 of 10 ( Start time: 06:21:10 PM ) Total Marks: 1 A heap is a left-complete binary tree that conforms to the ___________ Select correct option: increasing order only decreasing order only heap order (log n) order
MC090406557 : Nadia Parveen Quiz Start Time: 06:18 PM Time Left 77 sec(s) Question # 5 of 10 ( Start time: 06:21:39 PM ) Total Marks: 1 A (an) _________ is a left-complete binary tree that conforms to the heap order Select correct option: heap binary tree binary search tree array MC090406557 : Nadia Parveen Quiz Start Time: 06:18 PM Time Left 72 sec(s) Question # 6 of 10 ( Start time: 06:22:04 PM ) Total Marks: 1 Divide-and-conquer as breaking the problem into a small number of Select correct option: pivot Sieve smaller sub problems Selection
MC090406557 : Nadia Parveen Quiz Start Time: 06:18 PM Time Left 48 sec(s) Question # 7 of 10 ( Start time: 06:22:40 PM ) Total Marks: 1 In Sieve Technique we do not know which item is of interest Select correct option: True False MC090406557 : Nadia Parveen Quiz Start Time: 06:18 PM Time Left 34 sec(s) Question # 8 of 10 ( Start time: 06:23:26 PM ) Total Marks: 1 The recurrence relation of Tower of Hanoi is given below T(n)={1 if n=1 and 2T(n-1) if n >1 In order to move a tower of 5 rings from one peg to another, how many ring moves are required? Select correct option: 16 10 32 31 (yeh just tukka hai)
MC090406557 : Nadia Parveen Quiz Start Time: 06:18 PM Time Left 36 sec(s) Question # 9 of 10 ( Start time: 06:24:44 PM ) Total Marks: 1 In the analysis of Selection algorithm, we eliminate a constant fraction of the array with each phase; we get the convergent _______________ series in the analysis, Select correct option: linear arithmetic geometric (yeh b gup hi lugti hai) exponent MC090406557 : Nadia Parveen Quiz Start Time: 06:18 PM Time Left 76 sec(s) Question # 10 of 10 ( Start time: 06:25:43 PM ) Total Marks: 1 For the heap sort, access to nodes involves simple _______________ operations. Select correct option: arithmetic binary algebraic logarithmic (bongi hai...) Question # 1 of 10 ( Start time: 10:02:41 PM ) Total Marks: 1For the sieve technique we solve the problem,Select correct option:
recursivelymathematicallypreciselyaccuratelyThe sieve technique works in ___________ as followsSelect correct option:phasesnumbersintegersroutinesSlow sorting algorithms run in,Select correct option:T(n^2)T(n)T( log n)A (an) _________ is a left-complete binary tree that conforms to the heap orderSelect correct option:heapbinary treebinary search treearray
In the analysis of Selection algorithm, we eliminate a constant fraction of the array with each phase; we get the convergent _______________ series in the analysis,Select correct option:lineararithmeticgeometricexponent
In the analysis of Selection algorithm, we make a number of passes, in fact it could be as many as,Select correct option:T(n)T(n / 2)log nn / 2 + n / 4
The sieve technique is a special case, where the number of sub problems is just Select correct option:5many1few
In which order we can sort?
Select correct option:increasing order onlydecreasing order onlyincreasing order or decreasing orderboth at the same time
The recurrence relation of Tower of Hanoi is given below T(n)={1 if n=1 and 2T(n-1) if n >1 In order to move a tower of 5 rings from one peg to another, how many ring moves are required?Select correct option:16103231
Analysis of Selection algorithm ends up with,Select correct option:T(n)T(1 / 1 + n)T(n / 2)T((n / 2) + n)
Last message received on 10/13 at 12:43 AMKhanjee: We do sorting to, Select correct option:
keep elements in random positions keep the algorithm run in linear order keep the algorithm run in (log n) order keep elements in increasing or decreasing order
Khanjee: Divide-and-conquer as breaking the problem into a small number of Select correct option:
pivot Sieve smaller sub problems Selection
The analysis of Selection algorithm shows the total running time is indeed ________in n, Select correct option:
arithmetic geometric linear orthogonal
How many elements do we eliminate in each time for the Analysis of Selection algorithm? Select correct option:
n / 2 elements (n / 2) + n elements n / 4 elements 2 n elements
Sieve Technique can be applied to selection problem? Select correct option:
True
For the heap sort we store the tree nodes in Select correct option:
level-order traversal in-order traversal pre-order traversal post-order traversal
1-One of the clever aspects of heaps is that they can be stored in arrays without using any _______________.
pointers **
constants
variables
functions
2- For the heap sort we store the tree nodes in
level-order traversal**
in-order traversal
pre-order traversal
post-order traversal
3- The sieve technique works in ___________ as follows
phases
numbers
integers ** not confrm
routines
4- In the analysis of Selection algorithm, we eliminate a constant fraction of the array with each phase; we get the convergent _______________ series in the analysis,
linear
arithmetic
geometric **
exponent
5- We do sorting to,
keep elements in random positions
keep the algorithm run in linear order
keep the algorithm run in (log n) order
keep elements in increasing or decreasing order ***
6- In the analysis of Selection algorithm, we make a number of passes, in fact it could be as many as,
T(n)
T(n / 2)***
log n
n / 2 + n / 4
7- In which order we can sort?
increasing order only
decreasing order only
increasing order or decreasing order ***
both at the same time
8- In Sieve Technique we do not know which item is of interest
True**
False
9- For the sieve technique we solve the problem,
recursively**
mathematically
precisely
10- Divide-and-conquer as breaking the problem into a small number of
pivot
Sieve
smaller sub problems **
Selection
Question # 1 of 10 Total Marks: 1Divide-and-Conquer is as breaking the problem into a small number of· Smaller Sub Problems· Pivot· Sieve· SolutionsQuestion # 2 of 10 Total Marks: 1Analysis of Selection Sort ends up with· T(n)· T(1/1+n)· T(n/2)· T((n/2) +n)
Question # 3 of 10 Total Marks: 1How many elements do we eliminate each time for the Analysis of SelectionAlgorithm?· (n / 2)+n Elements· n / 2 Elements· n / 4 Elements· 2 n ElementsQuestion # 4 of 10 Total Marks: 1A heap is a left-complete binary tree that conforms to the ?· Increasing Order· Decreasing order· Heap Order· (nlog n) orderQuestion # 5 of 10 Total Marks: 1The Sieve Sequence is a special case where the number of smaller sub problems isjust_ .· 4· Many· 1· FewImrangeeQuestion # 6 of 10 Total Marks: 1Heaps can be stored in arrays without using any pointers this is due to the of the binarytree?· Tree Nodes· Right-Complete Nature· Left-Complete Nature· Tree LeavesQuestion # 7 of 10 Total Marks: 1For the Heap Sort access to nodes involves simple _ operations:· Geometric· Linear· Arithmetic· AlgebraicQuestion # 8 of 10 Total Marks: 1The Analysis of Selection Sort shows that the total running time is indeed in n?· Geometric· Linear· Arithmetic
· AlgebraicQuestion # 9 of 10 Total Marks: 1For the sieve technique we solve the problem· Recursively· Randomly· Mathematically· PreciselyQuestion # 10 of 10 Total Marks: 1How much time merger sort takes for an array of numbers?· T(n^2)· T(n)· T(log n)· T(n log n)MC090406505 :
Quiz Start Time: 06:48 PM
Time Left 86 sec(s)
Question # 1 of 10 ( Start time: 06:48:26 PM ) Total Marks: 1
How many elements do we eliminate in each time for the Analysis of Selection algorithm?
Select correct option:
MC090406505 : Time Left 83
Quiz Start Time: 06:48 PM
sec(s)
Question # 2 of 10 ( Start time: 06:49:01 PM ) Total Marks: 1
The recurrence relation of Tower of Hanoi is given below T(n)={1 if n=1 and 2T(n-1) if n >1 In order to move a tower of 5 rings from one peg to another, how many ring moves are required?
Select correct option:
MC090406505 :
Quiz Start Time: 06:48 PM
Time Left 85 sec(s)
Question # 3 of 10 ( Start time: 06:49:38 PM ) Total Marks: 1
The number of nodes in a complete binary tree of height h is
Select correct option:
MC090406505
Quiz Start Time: 06:48 PM
Time Left 87 sec(s)
Question # 4 of 10 ( Start time: 06:50:58 PM ) Total Marks: 1
One of the clever aspects of heaps is that they can be stored in arrays without using any _______________.
Select correct option:
MC090406505 : Time Left 83
Quiz Start Time: 06:48 PM
sec(s)
Question # 5 of 10 ( Start time: 06:51:24 PM ) Total Marks: 1
We do sorting to,
Select correct option:
MC090406505 :
Quiz Start Time: 06:48 PM
Time Left 87 sec(s)
Question # 6 of 10 ( Start time: 06:52:04 PM ) Total Marks: 1
In Sieve Technique we do not know which item is of interest
Select correct option:
MC090406505 :
Quiz Start Time: 06:48 PM
Time Left 83 sec(s)
Question # 7 of 10 ( Start time: 06:52:27 PM ) Total Marks: 1
Consider the following Algorithm: Fun(n){ if (n=1) return 1 else return (n * Fun(n-1)) } Recurrence for the above algorithm is:
Select correct option:
MC090406505 :
Quiz Start Time: 06:48 PM
Time Left 85 sec(s)
Question # 8 of 10 ( Start time: 06:53:56 PM ) Total Marks: 1
In the analysis of Selection algorithm, we make a number of passes, in fact it could be as many as,
Select correct option:
MC090406505 :
Quiz Start Time: 06:48 PM
Time Left 84 sec(s)
Question # 9 of 10 ( Start time: 06:54:25 PM ) Total Marks: 1
The reason for introducing Sieve Technique algorithm is that it illustrates a very important special case of,
Select correct option:
MC090406505 : Time Left 84
Quiz Start Time: 06:48 PM
sec(s)
Question # 9 of 10 ( Start time: 06:54:25 PM ) Total Marks: 1
The reason for introducing Sieve Technique algorithm is that it illustrates a very important special case of,
Select correct option:
MC090406505 :
Quiz Start Time: 06:48 PM
Time Left 80 sec(s)
Question # 10 of 10 ( Start time: 06:54:55 PM ) Total Marks: 1
In which order we can sort?
Select correct option:
1 - What type of instructions Random Access Machine (RAM) can execute? Choose best answer
1. Algebraic and logic 2. Geometric and arithmetic 3. Arithmetic and logic 4. Parallel and recursive
Correct Choice : 3 From Lectuer # 1 www.vugujranwala.com
2 - Random access machine or RAM is a/an
1. Machine build by Al-Khwarizmi 2. Mechanical machine 3. Electronics machine 4. Mathematical model
Correct Choice : 4 From Lectuer # 1 www.vugujranwala.com
3 - _______________ is a graphical representation of an algorithm
1. Segma Notation 2. Thita Notation 3. Flowchart 4. Asymptotic notation
Correct Choice : 3 From Lectuer # 2 www.vugujranwala.com
4 - What will be the total number of max comparisons if we run brute-force maxima algorithm with n elements?
1. n^2 2. n^n/2 3. n 4. n^8
Correct Choice : 1 From Lectuer # 3 www.vugujranwala.com
5 - function is given like 4n^4+ 5n^3+n what is the run time of this
1. theata(n^4) 2. theata(n^3) 3. theata(4n^4+ 5n^3) 4. theata(4n^4+ 5n^3)
Correct Choice : 1 From Lectuer # 4 www.vugujranwala.com
6 - Consider the following code: For(j=1; j
www.vugujranwala.com
7 - Execution of the following code fragment int i = N; while (i > 0)
{ int Sum = 0; int j; for (j = 0; j Sum++; cout
www.vugujranwala.com
8 - Let us say we have an algorithm that carries out N2 operations for an input of size N. Let us say that a computer takes 1 microsecond (1/1000000 second) to carry out one operation. How long does the algorithm run for an input of size 3000?
1. 90 seconds 2. 9 seconds 3. 0.9 seconds 4. 0.09 seconds
Correct Choice : 2 From Lectuer # 4 www.vugujranwala.com
9 - The appropriate big thita classification of the given function. f(n) = 4n2 + 97n + 1000 is
1. ?(n) 2. O(2^n) 3. O(n^2) 4. O(n^2logn)
Correct Choice : 3 From Lectuer # 4 www.vugujranwala.com
10 - The appropriate big ? classification of the given function. f(n) = 4n2 + 97n + 1000 is
1. ?(n) 2. O(2^n) 3. O(n^2) 4. O(n^2logn)
Correct Choice : 3 From Lectuer # 4 www.vugujranwala.com
11 - Which sorting algorithm is faster
1. O (n log n) 2. O n^2 3. O (n+k) 4. O n^3
Correct Choice : 3 From Lectuer # 5 www.vugujranwala.com
12 - If algorithm A has running time 7n^2 + 2n + 3 and algorithm B has running time 2n^2, then
1. Both have same asymptotic time complexity 2. A is asymptotically greater 3. B is asymptotically greater 4. None of others
Correct Choice : 1 From Lectuer # 6 www.vugujranwala.com
13 - If algorithm A has running time 7n^2 + 2n + 3 and algorithm B has running time 2n^2, then
1. Both have same asymptotic time complexity 2. A is asymptotically greater 3. B is asymptotically greater 4. None of others
Correct Choice : 1 From Lectuer # 6 www.vugujranwala.com
14 - What is the solution to the recurrence T(n) = T(n/2)+n .
1. O(logn) 2. O(n) 3. O(nlogn) 4. O(n^2)
Correct Choice : 1 From Lectuer # 8 www.vugujranwala.com
15 - How much time merge sort takes for an array of numbers?
1. (n^2) 2. T(n) 3. T( log n) 4. T(n log n)
Correct Choice : 2 From Lectuer # 8 www.vugujranwala.com
www.vugujranwala.com
17 - Consider the following Algorithm: Factorial (n){ if (n=1)
return 1 else return (n * Factorial(n-1))
} Recurrence for the following algorithm is:
1. T(n) = T(n-1) +1 2. T(n) = nT(n-1) +1 3. T(n)= T(n-1) +n 4. T(n)=T(n(n-1)) +1
Correct Choice : 4 From Lectuer # 9 www.vugujranwala.com
18 - For the Sieve Technique we take time
1. T(nk) . 2. T(n / 3)
3. n^2 4. n/3
Correct Choice : 1 From Lectuer # 10 www.vugujranwala.com
www.vugujranwala.com
20 - Sieve Technique applies to problems where we are interested in finding a single item from a larger set of _____________
1. n items 2. phases 3. pointers 4. constant
Correct Choice : 1 From Lectuer # 10 www.vugujranwala.com
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22 - In Sieve Technique we do not know which item is of interest
1. FALSE 2. TRUE 3. 4.
Correct Choice : 2 From Lectuer # 10 www.vugujranwala.com
23 - For the sieve technique we solve the problem,
1. recursively 2. mathematically 3. accurately 4. precisely
Correct Choice : 1 From Lectuer # 10 www.vugujranwala.com
24 - For the Sieve Technique we take time
1. T(nk) 2. T(n / 3) 3. n^2 4. n/3
Correct Choice : 1 From Lectuer # 10 www.vugujranwala.com
25 - How many elements do we eliminate in each time for the Analysis of Selection algorithm?
1. n / 2 elements 2. (n / 2) + n elements 3. n / 4 elements 4. n elements
Correct Choice : 4 From Lectuer # 10 www.vugujranwala.com
26 - Sieve Technique applies to problems where we are interested in finding a single item from a larger set of _____________
1. n items 2. phases 3. pointers 4. constant
Correct Choice : 1 From Lectuer # 10 www.vugujranwala.com
27 - Sieve Technique can be applied to selection problem?
1. TRUE 2. FALSE 3. 4.
Correct Choice : 1 From Lectuer # 10 www.vugujranwala.com
28 - The analysis of Selection algorithm shows the total running time is indeed ________in n,
1. arithmetic 2. geometric 3. linear 4. orthogonal
Correct Choice : 3 From Lectuer # 10 www.vugujranwala.com
29 - The reason for introducing Sieve Technique algorithm is that it illustrates a very important special case of,
1. divide-and-conquer 2. decrease and conquer 3. greedy nature 4. 2-dimension Maxima
Correct Choice : 1 From Lectuer # 10 www.vugujranwala.com
30 - The sieve technique works in ___________ as follows
1. phases 2. numbers 3. integers 4. routines
Correct Choice : 1 From Lectuer # 10 www.vugujranwala.com
31 - The sieve technique works in ___________ as follows
1. phases
2. numbers 3. integers 4. routines
Correct Choice : 1 From Lectuer # 10 www.vugujranwala.com
32 - A (an) _________ is a left-complete binary tree that conforms to the heap order
1. heap 2. binary tree 3. binary search tree 4. array
Correct Choice : 1 From Lectuer # 11 www.vugujranwala.com
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34 - For the heap sort, access to nodes involves simple _______________ operations.
1. arithmetic 2. binary 3. algebraic 4. logarithmic
Correct Choice : 1 From Lectuer # 11 www.vugujranwala.com
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37 - We do sorting to,
1. keep elements in random positions 2. keep the algorithm run in linear order 3. keep the algorithm run in (log n) order 4. keep elements in increasing or decreasing order
Correct Choice : 1 From Lectuer # 11 www.vugujranwala.com
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42 - For the heap sort we store the tree nodes in
1. level-order traversal 2. in-order traversal 3. pre-order traversal 4. post-order traversal
Correct Choice : 1 From Lectuer # 11 www.vugujranwala.com
www.vugujranwala.com 44 - In the analysis of Selection algorithm, we make a number of passes, in fact it could be as
many as,
1. T(n) 2. T(n / 2) 3. log n 4. n / 2 + n / 4
Correct Choice : 3 From Lectuer # 11 www.vugujranwala.com
45 - In the analysis of Selection algorithm, we make a number of passes, in fact it could be as many as,
1. T(n) 2. T(n / 2) 3. log n 4. n / 2 + n / 4
Correct Choice : 3 From Lectuer # 11 www.vugujranwala.com
46 - In which order we can sort?
1. increasing order only 2. decreasing order only 3. increasing order or decreasing order 4. both at the same time
Correct Choice : 3 From Lectuer # 11 www.vugujranwala.com
47 - One of the clever aspects of heaps is that they can be stored in arrays without using any _______________.
1. pointers 2. constants 3. variables 4. functions
Correct Choice : 1 From Lectuer # 11 www.vugujranwala.com
48 - One of the clever aspects of heaps is that they can be stored in arrays without using any _______________.
1. pointers 2. constants 3. variables 4. functions
Correct Choice : 1 From Lectuer # 11 www.vugujranwala.com
49 - Slow sorting algorithms run in,
1. O(n^2)
2. O(n) 3. O( log n) 4. O(n log n)
Correct Choice : 1 From Lectuer # 11 www.vugujranwala.com
50 - What is the total time to heapify?
1. ?(log n) 2. ?(n log n) 3. ?(n^2 log n) 4. ?(log^2n)
Correct Choice : 1 From Lectuer # 12 www.vugujranwala.com
-When we call heapify then at each level the comparison performed takes time It will take O (1)
1. Time will vary according to the nature of input data 2. It can not be predicted 3. It will take O (log n) 4. None of the Given
Correct Choice : 3 From Lectuer # 12 www.vugujranwala.com
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53 - After partitioning array in Quick sort, pivot is placed in a position such that
1. Values smaller than pivot are on left and larger than pivot are on right 2. Values larger than pivot are on left and smaller than pivot are on right 3. Pivot is the first element of array 4. Pivot is the last element of array
Correct Choice : 2 From Lectuer # 13 www.vugujranwala.com
54 - The running time of quick sort depends heavily on the selection of
1. No of inputs 2. Arrangement of elements in array 3. Size o elements 4. Pivot element
Correct Choice : 4 From Lectuer # 13 www.vugujranwala.com
55 - In Quick Sort Constants hidden in T(n log n) are
1. Large 2. Medium 3. Small 4. Not Known
Correct Choice : 3 From Lectuer # 14 www.vugujranwala.com
56 - In Quick Sort Constants hidden in T(n log n) are
1. Large 2. Medium 3. Small 4. Not Known
Correct Choice : 3 From Lectuer # 14 www.vugujranwala.com
57 - Is it possible to sort without making comparisons?
1. Yes 2. No 3. 4.
Correct Choice : 1 From Lectuer # 15 www.vugujranwala.com
58 - Merge sort is stable sort, but not an in-place algorithm
1. TRUE 2. FALSE 3. 4.
Correct Choice : 1 From Lectuer # 15 www.vugujranwala.com
59 - In counting sort, once we know the ranks, we simply _________ numbers to their final positions in an output array.
1. Delete 2. copy 3. Mark 4. arrange
Correct Choice : 2 From Lectuer # 15 www.vugujranwala.com
60 - An in place sorting algorithm is one that uses ___ arrays for storage
1. Two dimensional arrays 2. More than one array 3. No Additional Array 4. None of the above
Correct Choice : 3 From Lectuer # 15 www.vugujranwala.com
61 - Continuation/counting sort is suitable to sort the elements in range 1 to k
1. K is Large 2. K is not known 3. K may be small or large 4. K is small
Correct Choice : 4 From Lectuer # 15 www.vugujranwala.com
62 - In stable sorting algorithm.
1. If duplicate elements remain in the same relative position after sorting 2. One array is used 3. More than one arrays are required 4. Duplicating elements not handled
Correct Choice : 1 From Lectuer # 15 www.vugujranwala.com
63 - One example of in place but not stable algorithm is
1. Merger Sort 2. Quick Sort 3. Continuation Sort 4. Bubble Sort
Correct Choice : 2 From Lectuer # 15 www.vugujranwala.com
64 - One example of in place but not stable algorithm is
1. Merger Sort 2. Quick Sort 3. Continuation Sort 4. Bubble Sort
Correct Choice : 2 From Lectuer # 15 www.vugujranwala.com
65 - One of the clever aspects of heaps is that they can be stored in arrays without using any _______________.
1. pointers 2. constants 3. variables 4. functions
Correct Choice : 1
66 - Quick sort is
1. Stable & in place 2. Not stable but in place 3. Stable but not in place
From Lectuer # 15 www.vugujranwala.com
4. Some time stable & some times in place Correct Choice : 3 From Lectuer # 15
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67 - Quick sort is
1. Stable & in place 2. Not stable but in place 3. Stable but not in place
4. Some time stable & some times in place Correct Choice : 2 From Lectuer # 15
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68 - Which may be a stable sort?
1. Merger 2. Insertion 3. Both above 4. None of the above
Correct Choice : 3 From Lectuer # 15 www.vugujranwala.com
69 - Which of the following sorting algorithms is stable? (i) Merge sort, (ii) Quick sort, (iii) Heap sort, (iv) Counting Sort.
1. Only i 2. Only ii 3. Both i and ii 4. Both iii and iv
Correct Choice : 1 From Lectuer # 15 www.vugujranwala.com
70 - Which of the following sorting algorithms is stable? (i) Merge sort, (ii) Quick sort, (iii) Heap sort, (iv) Counting Sort.
1. Only i 2. Only ii 3. Both i and ii 4. Both iii and iv
Correct Choice : 1 From Lectuer # 15 www.vugujranwala.com
71 - Mergesort is a stable algorithm but not an in-place algorithm.
1. TRUE 2. FALSE 3. 4.
Correct Choice : 1 From Lectuer # 16 www.vugujranwala.com
72 - Memorization is?
1. To store previous results for future use 2. To avoid this unnecessary repetitions by writing down the results of recursive
calls and looking them up again if we need them later 3. To make the process accurate 4. None of the above
Correct Choice : 2 From Lectuer # 16 www.vugujranwala.com
73 - Dynamic programming algorithms need to store the results of intermediate sub-problems.
1. TRUE 2. FALSE 3. 4.
Correct Choice : 1 From Lectuer # 17 www.vugujranwala.com
74 - Dynamic programming uses a top-down approach.
1. TRUE 2. FALSE 3. 4.
Correct Choice : 2 From Lectuer # 17 www.vugujranwala.com
75 - The edit distance between FOOD and MONEY is
1. At most four 2. At least four 3. Exact four 4. Wrong
Correct Choice : 1 From Lectuer # 17 www.vugujranwala.com
76 - The edit distance between FOOD and MONEY is
1. At most four 2. At least four 3. Exact four 4. Wrong
Correct Choice : 1 From Lectuer # 17 www.vugujranwala.com
77 - If there are O (n^2) entries in edit distance matrix then the total running time is
1. O (1) 2. O (n^2) 3. O (n) 4. O (n log n)
Correct Choice : 2 From Lectuer # 18 www.vugujranwala.com
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79 - A p x q matrix A can be multiplied with a q x r matrix B. The result will be a p x r matrix C. There are (p . r) total entries in C and each takes _________ to compute.
1. O (q) 2. O (1) 3. O (n^2) 4. O (n^3)
Correct Choice : 1 From Lectuer # 19 www.vugujranwala.com
80 - For Chain Matrix Multiplication we can not use divide and conquer approach because,
1. We do not know the optimum k 2. We use divide and conquer for sorting only 3. We can easily perform it in linear time 4. Size of data is not given
Correct Choice : 1 From Lectuer # 19 www.vugujranwala.com
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82 - A p x q matrix A can be multiplied with a q x r matrix B. The result will be a p x r matrix C. There are (p . r) total entries in C and each takes _________ to compute.
1. O (q) 2. O (1) 3. O (n^2) 4. O (n^3)
Correct Choice : 1 From Lectuer # 19 www.vugujranwala.com
83 - The Knapsack problem belongs to the domain of _______________ problems.
1. Optimization 2. NP Complete 3. Linear Solution 4. Sorting
Correct Choice : 1 From Lectuer # 21 www.vugujranwala.com
84 - Suppose we have three items as shown in the following table, and suppose the
capacity of the knapsack is 50 i.e. W = 50. Item Value Weight 1 60 10 2 100 20 3 120 30 The optimal solution is to pick
1. Items 1 and 2 2. Items 1 and 3 3. Items 2 and 3 4. None of these
Correct Choice : 3 From Lectuer # 21 www.vugujranwala.com
85 - Huffman algorithm uses a greedy approach to generate a postfix code T that minimizes the expected length B (T) of the encoded string.
1. TRUE 2. FALSE 3. 4.
Correct Choice : 1 From Lectuer # 22 www.vugujranwala.com
86 - The codeword assigned to characters by the Huffman algorithm have the property that no codeword is the postfix of any other.
1. TRUE 2. FALSE 3. 4.
Correct Choice : 2 From Lectuer # 22 www.vugujranwala.com
87 - The greedy part of the Huffman encoding algorithm is to first find two nodes with larger frequency.
1. TRUE 2. FALSE 3. 4.
Correct Choice : 2 From Lectuer # 22 www.vugujranwala.com
88 - An optimization problem is one in which you want to find,
1. Not a solution 2. An algorithm 3. Good solution 4. The best solution
Correct Choice : 4 From Lectuer # 22